(* Content-type: application/mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 7.0' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       145,          7]
NotebookDataLength[      6997,        218]
NotebookOptionsPosition[      6666,        202]
NotebookOutlinePosition[      7011,        217]
CellTagsIndexPosition[      6968,        214]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{

Cell[CellGroupData[{
Cell[BoxData[{
 RowBox[{
  RowBox[{
   RowBox[{"a", "[", 
    RowBox[{"{", 
     RowBox[{"x_", ",", "y_"}], "}"}], "]"}], "=", 
   RowBox[{
    TagBox[
     RowBox[{"(", "\[NoBreak]", GridBox[{
        {"1", "0"},
        {"2", 
         RowBox[{"-", "1"}]}
       },
       GridBoxAlignment->{
        "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
         "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.7]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
     Function[BoxForm`e$, 
      MatrixForm[BoxForm`e$]]], ".", 
    TagBox[
     RowBox[{"(", "\[NoBreak]", 
      TagBox[GridBox[{
         {"x"},
         {"y"}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.5599999999999999]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}],
       Column], "\[NoBreak]", ")"}],
     Function[BoxForm`e$, 
      MatrixForm[BoxForm`e$]]]}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"b", "[", 
    RowBox[{"{", 
     RowBox[{"x_", ",", "y_"}], "}"}], "]"}], "=", 
   RowBox[{
    RowBox[{
     TagBox[
      RowBox[{"(", "\[NoBreak]", GridBox[{
         {"3", "0"},
         {
          RowBox[{"-", "1"}], "2"}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.7]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
      Function[BoxForm`e$, 
       MatrixForm[BoxForm`e$]]], ".", 
     TagBox[
      RowBox[{"(", "\[NoBreak]", 
       TagBox[GridBox[{
          {"x"},
          {"y"}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.5599999999999999]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}],
        Column], "\[NoBreak]", ")"}],
      Function[BoxForm`e$, 
       MatrixForm[BoxForm`e$]]]}], "+", 
    TagBox[
     RowBox[{"(", "\[NoBreak]", 
      TagBox[GridBox[{
         {"1"},
         {"1"}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.5599999999999999]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}],
       Column], "\[NoBreak]", ")"}],
     Function[BoxForm`e$, 
      MatrixForm[BoxForm`e$]]]}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"c", "[", 
    RowBox[{"{", 
     RowBox[{"x_", ",", "y_"}], "}"}], "]"}], "=", 
   RowBox[{"MatrixForm", "[", 
    RowBox[{"Simplify", "[", 
     RowBox[{
      RowBox[{"Composition", "[", 
       RowBox[{"a", ",", "b", ",", "a", ",", "b", ",", "a"}], "]"}], "[", 
      RowBox[{"{", 
       RowBox[{"x", ",", "y"}], "}"}], "]"}], "]"}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"d", "[", 
    RowBox[{"{", 
     RowBox[{"x_", ",", "y_"}], "}"}], "]"}], "=", 
   RowBox[{"MatrixForm", "[", 
    RowBox[{"Simplify", "[", 
     RowBox[{
      RowBox[{"Composition", "[", 
       RowBox[{"b", ",", "a", ",", "a", ",", "b", ",", "b"}], "]"}], "[", 
      RowBox[{"{", 
       RowBox[{"x", ",", "y"}], "}"}], "]"}], "]"}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{"X", " ", "=", " ", 
  RowBox[{
   RowBox[{"Composition", "[", 
    RowBox[{"c", ",", "d", ",", "c", ",", "c", ",", "d", ",", "c", ",", "d"}],
     "]"}], "[", 
   RowBox[{"{", 
    RowBox[{"x", ",", "y"}], "}"}], "]"}]}]}], "Input",
 CellChangeTimes->{{3.552424328732464*^9, 3.552424351602496*^9}, {
  3.552424465832656*^9, 3.5524245313637476`*^9}, {3.5524245956338377`*^9, 
  3.552424620263872*^9}}],

Cell[BoxData[
 RowBox[{"c", "[", 
  RowBox[{"d", "[", 
   RowBox[{"c", "[", 
    RowBox[{"c", "[", 
     RowBox[{"d", "[", 
      RowBox[{"c", "[", 
       TagBox[
        RowBox[{"(", "\[NoBreak]", 
         TagBox[GridBox[{
            {
             RowBox[{"13", "+", 
              RowBox[{"27", " ", "x"}]}]},
            {
             RowBox[{"1", "-", 
              RowBox[{"19", " ", "x"}], "+", 
              RowBox[{"8", " ", "y"}]}]}
           },
           
           GridBoxAlignment->{
            "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
             "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
           GridBoxSpacings->{"Columns" -> {
               Offset[0.27999999999999997`], {
                Offset[0.5599999999999999]}, 
               Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
               Offset[0.2], {
                Offset[0.4]}, 
               Offset[0.2]}, "RowsIndexed" -> {}}],
          Column], "\[NoBreak]", ")"}],
        Function[BoxForm`e$, 
         MatrixForm[BoxForm`e$]]], "]"}], "]"}], "]"}], "]"}], "]"}], 
  "]"}]], "Output",
 CellChangeTimes->{3.552424586773825*^9, 3.552424621013873*^9}]
}, Open  ]]
},
WindowSize->{1105, 465},
WindowMargins->{{Automatic, 78}, {Automatic, 8}},
FrontEndVersion->"7.0 for Microsoft Windows (64-bit) (November 10, 2008)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[CellGroupData[{
Cell[567, 22, 4897, 142, 136, "Input"],
Cell[5467, 166, 1183, 33, 43, "Output"]
}, Open  ]]
}
]
*)

(* End of internal cache information *)